Talk:Eötvös effect

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The opening section of this article has been copied from the article that is refererenced I have corresponded with Anders Persson via email, and I have his permission to use text of him that is publicly accessable for Wikipedia. --Cleonis | Talk 22:27, 11 January 2006 (UTC)

Contents 1 The standard approach 2 clarification below picture 3 Mercury mirror 3.1 Comparing two diagrams 4 A single centripetal force 5 Some arithmatic with the accelerations 6 Angular mechanics visualisations 7 A gravito-meter on a mercury mirror dish 8 Cleanup 9 The reason for the revert nov 9 10 More than one definition of Coriolis effect in circulation 11 No original research but compliance with modern standards

[edit] The standard approach

The standard approach as I learned, is not to use centripetal force, but centripetal acceleration. The weight depends on the difference g-a. Harald88 22:54, 11 January 2006 (UTC)

You are correct, and I have edited the article accordingly. The mass drops out of the equations. The Eötvös effect is the change of gravimetric readings. --Cleonis | Talk 10:50, 13 January 2006 (UTC)

[edit] clarification below picture

[copied from personal page:]

[Cleaonis wrote:] The poleward force, that is introduced in the Eötvös effect article, is obvious if the thinking is anchored on inertial space. Some people have argued to me that the resultant poleward force cannot actually exist. For, they said, if it would exist then all oceans would flow to the poles. It's tricky.

I dealt with that misunderstanding by adding a precision in the text in the drawing. Harald88 18:27, 15 January 2006 (UTC)

But I now see that now it is wrong! Sorry, but apparently you are confused now: objects including water that co-rotates are in full equilibrium. Harald88 18:30, 15 January 2006 (UTC)

That is what is stated in the article: the atmospheric layer of the earth is equally thick everywhere. The situation is comparable to the layer of mercury on the dish of a mercury mirror as is used in astronomy. (Currently the biggest mercury mirror has a diameter of 6 meters.) The shape of the dish is parabolic. The closer you get to the rim, the stronger the force on the mercury to flow to the center. When the dish is rotating at the designed angular velocity, the mercury redistributes itself into an even layer.--Cleonis | Talk 18:59, 15 January 2006 (UTC)

I maintain that it was misleading, and now simply erroneous; and that my version is correct:

The force of gravity, the normal force and the resultant poleward force for an object in rest in the inertial system

.

As you state yourself on my page: "There is definitely an equilibrium at play". However, in your drawing there is no equilibrium, because the centripetal acceleration is not accounted for. Harald88 21:44, 15 January 2006 (UTC)

There is an equilibrium at play. This equilibrium is not an equilibrium of forces, for in motion along a circular trajectory there is an unbalanced force at work: the centripetal force.

The rotation is around the Earth's axis, of course, so strictly speaking the blue arrow should have been drawn perpendicular to the Earth's axis, pointing towards the Earth's axis. But in general, most of the resulting motion is parallel to the surface. When a zeppelin is moving in east-to-west direction then there is a surplus of centripetal force, and this surplus of centripetal force will pull the zeppelin towards the nearest pole.

If I would have drawn the blue arrow in the correct direction, I would have had to decompose it into a component perpendicular to the local surface, and a component parallel to the local surface.

Generally I try to make pictures as uncluttered as possible. Generally, I try to use as few arrows as possible. Here, the blue arrow represents that a centripetal force is present and working. --Cleonis | Talk 23:54, 15 January 2006 (UTC)

Historically, Eötvös noticed the effect in relation to ships with a small velocity relative to the Earth. And only a supersonic aircraft can go fast enough to be at rest with respect to the inertial frame. The situations we are interested in are the situations with just a small velocity relative to the Earth --Cleonis | Talk 00:44, 16 January 2006 (UTC)

Supposing that your description is Newtonian, and not confusing the issue by making a fictuous description: The centripetal term from acceleration is lacking in this picture. If there were, and with the same simplicity, the one force arrow would correspond not to mg but to to m(g-a), and the forces relative to the earth surface would be balanced (and thus not illustrate what might push the zeppelin to the pole) -- it's the same issue as in the first discussion.

However you put it, this description here is approximately correct, while the one in the article is erroneous; the drawings are equally simple. A correct explanation is helpful, but an incorrect explanation only confuses; and illustrating extreme conditions is usually very effective. Harald88 08:08, 16 January 2006 (UTC)

I am very much puzzled by your answer. I don't see why you refer to a diagram in which forces are balanced. There is babylonian confusion going on here. I propose that we discuss the newtonian physcics of the rotating mercury mirror dish. In the case of the rotating mercury dish, the force of gravitation is uniform everywhere, that simplifies the matter. --Cleonis | Talk 08:38, 16 January 2006 (UTC)

I agree that if the diagram as a whole is drawn for the motion with respect to inertial space, then the blue arrow must be perpendicular to the Earth's axis. I can make a version with the blue arrow perpendicular, and state clearly that it is for motion with respect to inertial space. --Cleonis | Talk 09:01, 16 January 2006 (UTC)

[edit] Mercury mirror

There is the large Zenith telescope, currently the largest murcury mirror telescope, with a diameter of 6 meters.

Assuming the rotationn rate of the mirror is one revolution every 10 seconds, then the incline of the parabolic dish at the rim is about 7 degrees away from the horizontal. The rim is then a couple of decimeters higher than the center.

Do you agree with the following statements:
Due to the incline of the surface, there is at all points a centripetal force.
If the dish would slow down, that centripetal force would cause the mercury to flow to the center.
The centripetal force that is exerted on the mercury is unbalanced. The mercury exerts a reaction force on the dish, but that does not affect the motion of the mercury. --Cleonis | Talk 00:09, 16 January 2006 (UTC)

I disagree: there is only a centripetal force component when the disc slows down; otherwise the term g-a does not result in a centripetal force component (again the same issue as at the top of the page!) I hope to come back here another time, when I find the time to comment at it carefully. But I like your racecar track illustration, I think that is really appropriate and helpful. Harald88 20:53, 16 January 2006 (UTC)

Correction: I thought you to mean a centripetal force component of the mercury relative to the disc. Now I understand you to mean the centripetal force component of gravity that provides the necessary force to keep the mercury at rest relative to the disc. IOW, indeed a "Babylonian speech confusion", mostly because of lack of precision of our mutual statements. Harald88 07:58, 17 January 2006 (UTC)

For example: I am unfamiliar with the turn of phrase: "a centripetal force component of the mercury relative to the disc". It must mean something for you, but I haven't got a clue what that meaning is. --Cleonis | Talk 08:53, 17 January 2006 (UTC)

[edit] Comparing two diagrams

Let there be the dish for the 6 meter diameter mercury mirror telescope. The mercury is removed and a remote controlled toy car is steered over the surface. The toy car weighs precisely one kilogram.

1. Let the dish be rotating, and the toy car is stationary with respect to the dish. The toy car is close to the rim, so the toy car is at an incline of 7 degrees.
   Let a diagram be drawn for the forces that are acting on the toy car. There is a vertical arrow, pointing down, representing one kilogram of gravitational force on the toy car. And there is an arrow pointing upwards, but 7 degrees away from the vertical, representing 1.01 kilogram of normal force (the cosine of 7 degrees is 0.99, so the inverse is 1.01 ) Optional in the diagram is the resulting force of those two forces.
2. Let the dish be rotating, and let the toy compensate the rotation of the dish by going at a velocity of 1.88 meters per second with respect to the dish, making the toy stationary with respect to inertial space. Arrows in the diagram: there is a vertical arrow, pointing down, representing one kilogram of gravitational force on the toy car. There is an arrow pointing upwards, 7 degrees away from the vertical, the normal force: 1.01 kilogram of normal force. And thirdly, now there is an arrow for the grip of the tires of the toy car, and the arrow for that force is parallel to the local surface, and points away from the center. Those three forces balance each other

So of the two diagrams above only the first one is suitable for illustrating the Eötvös effect.

[edit] A single centripetal force

An even simpler case than the mercury mirror is two balls connected by a spring. The common center of mass of the two balls is in free-motion, let's say the circling balls are onboard a space-station. The motion of the two balls can be accounted for with a single force: a centripetal force that is exerted by the spring on the balls. --Cleonis | Talk 13:45, 16 January 2006 (UTC)

[edit] Some arithmatic with the accelerations

I copy and paste from above:

But I like your racecar track illustration, I think that is really appropriate and helpful. Harald88 20:53, 16 January 2006 (UTC)

I'm pretty sure by now that we actually don't disagree. I think any apparent dissent is babylonian confusion.

In the case of motion over the Equator, parallel to the equator, you were correct in pointing out that when a zeppelin is cruising at 490 m/s with respect to inertial space, instead of 465 m/s, that it is the centripetal acceleration that has changed.

The most refined gravito-meters are a tube that is pumped vacuum, and then a test mass is dropped, and the acceleration of the test mass is measured.

At the equator the gravitational acceleration g is 9.780 m/sec^2
The centripetal acceleration that corresponds to a velocity of 465 m/s with respect to inertial space and a radius of 6370 km is 0.034 m/sec^2
So the true gravitation at the equator is 9,780 + 0.034 = 9.814 m/sec^2
And what a gravito-meter measures is 9.780 m/sec^2
Naturally it is the measured acceleration that is the most useful for any science and engineering.
When a zeppelin moves at 490 m/s with respect to inertial space then the corresponding centripetal acceleration is 0.038 m/sec^2.
Hence a gravitometer onboard a zeppelin cruising at 490 m/s will measure a gravitational acceleration of 9,814 - 0.038 = 9,776 m/sec^2

The mathematical derivation section has been brought into accordance with that. I will try to amend the 'explanation of the cosine' section. --Cleonis | Talk 23:58, 16 January 2006 (UTC)

[edit] Angular mechanics visualisations

I copy and paste from above:

But I like your racecar track illustration, I think that is really appropriate and helpful. Harald88 20:53, 16 January 2006 (UTC)

Here are some other examples that I have used, and stil use, to visualize the physics taking place.

A velodrome is a racetrack specifically for bicycle races. A velodrome with a track length of 250 metres usually has straights of about 60 metres long, and U-turns with an inner radius of about 20 metres, and about 65 metres in length. The banking of the turns is 42 degrees.

What would you see if someone would try to race with a little one-seater hovercraft on a velodrome track? Then you can pretty much calculate the lap times in advance, for there is only one velocity that will allow the hovercraft to negotiate the 42 degrees banked turns. Too fast and he swings wide, too slow and he'll scrape the inside

And what about the Arecibo dish? Suppose that parabolic dish is very sturdy, and some people would organize hovercraft races that go round and round on the dish. The Arecibo dish has a diameter of 300 meters. Suppose a hovercraft is going round on that dish. Assuming that the rim is 30 meter higher than the center then it takes a hovercraft about 40 seconds to complete a full lap.

What happens when a racer opens up the throttle? Well, then he will swing wide, but his angular velocity won't change. On a parabolic dish, when you increase your velocity, you automatically climb to a higher trajectory, and a higher trajectory is a longer trajectory. All trajectories on a parabolic dish take the same amount of time to complete a full rotation. That is a property of harmonic oscillation For a given harmonic oscillator, the period of one oscillation is independent of the amplitude. --Cleonis | Talk 00:04, 17 January 2006 (UTC)

[edit] A gravito-meter on a mercury mirror dish

Let there be a mercury mirror dish, with a layer of mercury. A small gravito-meter is placed on the rotating mercury. (The gravito-meter is a vacuum tube, in which a test mass is dropped.) The small gravito-meter is floating on the mercury.

As the the gravito-meter is co-rotating with the dish and mercury, it will measure an acceleration perpendicular to the local mercury surface.

Let the dish slow down. Then the gravito-meter will slow down together with the mercury. The mercury will sag to the middle of the dish. In latitudinal direction, the gravito-meter will measure a deceleration. (If the test mass does not fall exactly parallel to the tube, then a sideways acceleration/deceleration is inferred.) In longitudinal direction the measured acceleration will remain perpendicular to the top surface of the mercury. --Cleonis | Talk 09:08, 17 January 2006 (UTC)

[edit] Cleanup

This article currently reads like an essay, not an encyclopedia article. I propose that the text be considerably shortened, removing all the numbers relating to velocities and masses of example vessels. In addition, the mathematical deduction is unnecessary. In my opinion, it is sufficient to link to the articles on Coriolis effect and centrifugal force respectively. --PeR 15:22, 9 November 2006 (UTC)

[edit] The reason for the revert nov 9

The statement that the second term of the correction formula for the Eötvös effect corresponds to the centrifugal term of the equation of motion for a rotating coordinate system is incorrect.

The centrifugal term is proportional to the square of the angular velocity of the rotating coordinate system with respect to the inertial coordinate system. On the other hand, the second term in the Eötvös correction formula is proportional to the squared velocity of the object with respect to the Earth.

Example: an object located at the equator that is stationary with respect to the Earth is circumnavigating the Earth's axis with a tangential velocity of about 465 meters per second. In the case of the equation of motion with respect to a coordinate system that is co-moving with the Earth, the centrifugal term is proportional to the square of 465.

In the examples given in the article, with an airship with cruising velocity of 25 m/s, it is clear that the value of 25 m/s does not correspond to the centrifugal term. --Cleonis | Talk 15:51, 9 November 2006 (UTC)

Read what you reverted again. The second term is due to the centrifugal force caused by the velocity of the airship (not to be confused with the centrifugal force caused by rotation of the Earth). Konwing that ω = v / r we have

Take away the m, because we're dealing with accelerations, not forces, and you get the second term of the Eötvös effect.

In addition, the text I inserted was paraphrasing Persson's article (page 7, the paragraph right below the formula.)

"The first term is the vertical Coriolis effect, the second term reflects the upward centrifugal effect of moving over any, even non-rotatig spherical surface."

--PeR 09:38, 10 November 2006 (UTC)

I think it is very confusing to the reader to claim that there are two different centrifugal forces.

In physics, when motion is mapped with respect to a rotating coordinate system, a centrifugal term is added to the equation of motion. This centrifugal term is proportional to the square of Ω the angular velocity of the rotating coordinate system with respect to the inertial coordinate system. This centrifugal term is referred to as the centrifugal force.

Another aspect is that the centrifugal term does not represent an actual force, the centrifugal term is a bookkeeping device. Using a rotating coordinate system introduces artifacts. For example, as seen from the Earth, Mars appears to go into retrograde motion from time to time. This is Apparent motion; there is no "retrograde pushing force" acting upon Mars. Likewise, when motion is mapped with respect to a rotating coordinate system, then a centrifugal term is introduced, but of course there is in fact no force in centrifugal direction being exerted upon the object.

Anyway, identifying the second term in the correction factor for the Eötvös effect with centrifugal force is incorrect. The expression Centrifugal force is associated with the angular velocity of the rotating coordinate system that is in use.

The reader should not be confused by stacking two different "centrifugal forces" on top of each other.

If you think that Persson's statement (in the article which you cited) is incorrect, feel free to look for another source. You are completely correct in saying that "centrifugal term does not represent an actual force". The same is true for the Coriolis force. The Eötvös force (which is the sum of these two) is hence also a fictitious force. This should be stated in the introduction. --PeR 11:54, 10 November 2006 (UTC)

The article does not claim the existence of an "Eötvös force". What the article describes is the Eötvös effect. For comparison: in quantum physics, the Casimir effect is recognized. There is a Casimir effect, but there is no Casimir force! Generally, the expression 'effect' is used when there is a specific, recognizable pattern at play. In the case of the Eötvös effect, the actual physical factors that are involved are gravity and inertia. --Cleonis | Talk 12:43, 10 November 2006 (UTC)

You can't sincerily claim that you don't understand what I mean by "Eötvös force" In the introduction that you copied from Persson you clearly state that the Eötvös effect accounts for apparent changes in gravity. Also, in the original version of the diagram below (p. 8) the arrows are labeled as "forces." --PeR 13:14, 10 November 2006 (UTC)

I referenced Persson's article because it is to my knowledge the only online available article that describes the Eötvös effect. However, I don't think Persson is using the expression 'centrifugal force' consistently. Sometimes he takes it to mean the centrifugal term in the equation of motion, and sometimes he takes centrifugal force to mean the total accelerometer reading, and those are two different things. I opted to avoid all that confusion by not referring to 'centrifugal force' at all. For describing the physics of the Eötvös effect, invoking 'centrifugal force' is not necessary. When something is not necessary, I don't invoke it. --Cleonis | Talk 12:53, 10 November 2006 (UTC)

The concept of centrifugal force is necessary to explain the second term. If you don't think that Persson's article is correct. Please don't write your own version of it on Wikipedia. It is against the WP:OR policy. Write your own article, and get it published in a peer-reviewed journal before putting any new theories here. --PeR 13:14, 10 November 2006 (UTC)

See my remark completely at the top of this page: in the standard textbook explanation of such problems there is a discussion of the vectorial acceleration g-a, which is usually positive.

If I'm not mistaken, the only real outward pointing force in this Newtonian picture is the normal force that the earth excerts on the ship, and this happens to be not a purely centrifugal force; also its centrifugal component does not by itself give information about the Eötvös effect.

In any case: in classical mechanics the use of the fictitious centrifugal force force is generally discouraged and rarely part of textbooks (there certainly is no need for it). Harald88 20:27, 10 November 2006 (UTC)

The use of the centrifugal force is discouraged in many undergraduate courses, simply because the use of non-inertial reference frames will cause the students problems to a larger extent than it simplifies things for them. (In actual fact it is the use of a rotating reference frame that is discouraged, until the students have the proper mathematical tools to handle it.) However, I've edited the text in a way that I hope will make everyone happy. --PeR 11:06, 11 November 2006 (UTC)

You misunderstood, sorry if this wasn't clear: here I mean mechanics textbooks that derive rotating frames and teach students how to work with them. Harald88 12:26, 11 November 2006 (UTC)

[edit] More than one definition of Coriolis effect in circulation

For meteorology, the factor that matters is the component that acts parallel to the local surface. Hence the Coriolis effect as taken into account in meteorology is described with a sine law. At the equator, the component parallel to the local surface is zero, hence at the equator meteorology does not take any Coriolis effect into account. (Advanced atmospheric models do need to take the Eötvös effect into account of course.)

To my knowledge, there is no standard name for the vector sum of the Coriolis effect and the Eötvös effect, which is why that arrow remains unnamed in the diagram. It would be convenient if there would be such a standard, but unfortunately there isn't. --Cleonis | Talk 16:09, 9 November 2006 (UTC)

[edit] No original research but compliance with modern standards

I copy and paste from above:

You can't sincerily claim that you don't understand what I mean by "Eötvös force" In the introduction that you copied from Persson you clearly state that the Eötvös effect accounts for apparent changes in gravity. Also, in the original version of the diagram below (p. 8) the arrows are labeled as "forces." --PeR 13:14, 10 November 2006 (UTC)

What is stated in the opening paragraph is that Eötvös noticed peculiarities in the gravimetric readings. Usually, a gravimeter that is taken along on journeys operates with a spring with a weight underneath. Stronger Earth gravity causes longer elongation of the spring. The spring provides the required amount of normal force. Depending on the amount of velocity with respect to the Earth, a different amount of normal force is required, and that is what is registered by the gravimeters. It would be very cumbersome to think of the Eötvös effect in terms of (apparently) altered gravity.

I deviated from Anders Persson's article to make the wikipedia article compliant with modern standards of physics education. Invoking centrifugal force as explanation is recommended against. --Cleonis | Talk 14:08, 12 November 2006 (UTC)